{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import lead_lag\n",
    "from lead_lag.scripts.read_bachelier_data import bachelier_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using synthetic data (Bachelier).\n"
     ]
    }
   ],
   "source": [
    "print('Using synthetic data (Bachelier).')\n",
    "x_with_ts, y_with_ts, true_lead_lag = bachelier_data()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ll = lead_lag.LeadLag(x_with_ts, y_with_ts, max_absolute_lag=400, verbose=False)\n",
    "ll.plot_data()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "ll.run_inference(multi_threading=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ll.plot_results()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correct lag = 200 Estimated lag = 200\n"
     ]
    }
   ],
   "source": [
    "print('Correct lag =', true_lead_lag, 'Estimated lag =', ll.lead_lag)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ll.llr > 0 # llr > 0 means that x leads and y follows."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
